1. Field of the Invention
The present invention relates to an apparatus for measuring particle size distribution and method to calculate particle size distribution of particles dispersed in a solvent.
2. Description of the Prior Art
Conventionally, there has been conducted a method for directing a laser light to particles dispersed in a solvent, detecting a scattered light from the particles by a detector, counting the detected scattered light to thereby measure the particle size distribution of the particles (which method is normally referred to as photon correlation spectroscopy (PCS)). With PCS, however, it is necessary to set some ranges of sampling time in advance and then measure the limits of the particle size ranges. In addition, to provide a wide measurement range for measuring large particles, it is necessary to make measurements while keeping the particles in a stable state for a long period. Besides, with this method, it is necessary to measure a particle size distribution in a diluted state so that scattered lights do not superpose one another.
To resolve these faults, there has been proposed measuring a particle size distribution by detecting an interference light due to scattered lights caused by the Doppler-shifted laser light directed to particles moving by Brownian motion and Fourier-transforming the detection signal of the interference light to thereby analyze the frequency. In general, in order to compute particle size distribution from power spectrum, an inverse problem for solving Category 1 Fredholm's integral equation which is a relative equation between the power spectrum, the response function, and the particle size distribution is performed.
For example, operation and display divisions by logarithmically dividing a measurement range into m sections are determined in advance. The particle size distribution F(D) (D=1 to m) indicating the number of particles of typical particle sizes in the operation/display section is obtained from light intensity frequency characteristics G. In other words, the relationship between frequency characteristics G(D) (D=1 to m) and the particle size distribution F(D) can be expressed as an equation of F=P.sup.-1 G, where P is a response function. The inverse matrix P.sup.-1 of the response function is obtained and F=P.sup.-1 G is operated to thereby acquire the particle size distribution F(D).
In this method, by calculating detection signals by Fourier-transform to get a power spectrum, the particle size distribution can be measured even if the number of particles present in a solvent is large and scattered lights superpose one another. Also, since a wide range measurement can be made for relatively short measurement time, fast and stable measurement is made possible compared to PCS.
It is desirable that the detection signal of an interference light which has been sampled at high speed is used in the power spectrum. Since the resultant data is wide in range, mass storage memory is required. Further, when subjecting the sampled data to deconvolution or inverse problem and the data in a wide range is used as it is, an operation unit requires a mass storage memory and high processing speed.
In consideration of this point, for example, in Japanese Patent Application Laid-open Publication No. 170844/1991 (hereinafter to be referred to as known example), deconvolution of power spectrum was practiced in such procedures that the power spectrum is converted into the form of convolution integration which can be readily inverted by linear transformation by converting the power spectrum into a logarithmic equal distance form, followed by inversion of it. That is to say, the power spectrum is converted by treating the frequency by logarithmic frequency, and the particle size by logarithmic particle size, by which a shift variant response function is made on non-dimensional logarithmic frequency axis, by which there was realized deconvolution integration with which operation can be processed in more simple procedure.
However, in case of converting the power spectrum into a logarithmic equal distance form, it has been unavoidable to thin out the majority part of the sampled data in the stage of converting into logarithmic equal distance.
FIG. 12A-D illustrate general processing methods for performing deconvolution operation or inverse problem from the detection signal of the measured interference light. FIG. 12A shows detection signals of scattered light, FIG. 12B shows a power spectrum (frequency distribution) which is calculated by the detection signals using Fourier transform, FIG. 12C shows a power spectrum calculated by a smoothing calculation from FIG. 12B after the scattered light has been smoothed. The power spectrum gives Lorentzian function indicating the intensity distribution of Brownian motion frequency in accordance with particle sizes. The power spectrum is subjected to deconvolution or inverse problem to thereby calculate a particle size or particle diameter distribution as shown in FIG. 12D.
In the power spectrum shown in FIG. 12B, however, there are influences such as the vibration noise of the solvent, white noise such as noise included in the output of the detector, the amplifier, and the electric circuit, or noise from the power supply line. Normally, the level of vibration noise is almost proportional to the inverse number of the frequency, so that a high level of noise tends to appear in low frequency areas in the power spectrum.
Due to this, if a particle size distribution is to be obtained from the power spectrum including the noise as shown in FIG. 12B, a particle size distribution Fs having different particle sizes and shifted from a true particle size distribution Ft indicated by a virtual line in FIG. 12D may be outputted or an immaterial particle size distribution Fg which does not originally exist may be outputted.
Considering this drawback, there is proposed removing the influence of noise as much as possible by, for example, integrating the power spectrum obtained as shown in FIG. 12C and the particle (diameter) size distribution and by performing smoothing. To remove noise with smoothing, however, it is necessary to carry out processing in a smoothing routine, which processing takes a lot of time. As a result, it has been difficult to make a real-time measurement with this method. Besides, with such smoothing performed, it is difficult to sufficiently remove the influence of noise in, particularly, a low frequency range and measurement accuracy has its limit.
In addition, if sampled data is selected at equal logarithmic intervals and the number of data points to be dealt with is reduced in order to increase processing speed, it is feared that errors may occur in the selection step as shown in FIG. 12C. That is, the power spectrum, shown by .circle-solid. marked points in FIG. 12C, has values of discontinuous intervals in accordance with sampling speed. Thus, while passing through true values indicated by a solid line, the .circle-solid. marked points do not often superpose on the O marked logarithmic selection points. For that reason, it is necessary to obtain the data of selection points which do not superpose on the .circle-solid. marked points by performing interpolation processing as indicated by a virtual line. The values obtained by this operation may be, however, shifted from actual values.
To avoid this drawback, the original data, which is converted into a power spectrum, may be sampled at a higher frequency. If the sampling frequency is high, it is required to employ components with higher-speed performance and the cost of the components increases accordingly. Thus, this method turns out to be impractical.
Moreover, as shown in an enlarged view B of FIG. 12C, where intervals of logarithmic selection points (O marked points) are wide, there often exist important portions for creating a power spectrum curve in the non-selected areas. Due to this, a polygonal line connecting selection points, as indicated by a two-dot chain line, may greatly differ from actual values. This has caused errors at the time of subjecting the particle size distribution to a deconvolution or an inverse problem.
Additionally, in the conventional deconvolution or inverse problem method using matrix calculation, vibration and divergence normally tend to occur when obtaining solutions of a particle size distribution matrix F. If vibration and divergence occur in a vector operation, immaterial peaks may be generated in the particle size distribution F. To prevent this, there is proposed adding a matrix to determine converging conditions for the distribution configuration and curve of the particle size distribution F. The matrix to determine converging conditions is difficult to acquire, resulting in complicated operation processing.
Further, the response function P varies according to measurement conditions such as the viscosity, refraction index and temperature of the solvent at the time of obtaining the particle size distribution F. As stated above, due to the need to perform complicated operation processing, there is no avoiding fixing the response function obtained as theoretical values and disadvantageously lowering the analysis accuracy of the method accordingly.
Moreover, in the above-stated inverse problem method, m operation and display sections obtained by logarithmically dividing a measurement range are set in advance and they are determined in accordance with the number of divided sections made by a detector and calculation conditions of the apparatus mentioned above. Since the number of divided sections made by a detector and the calculation conditions of the apparatus mentioned above are fixed, users cannot freely change operation and display sections. In other words, the users cannot widen an operation and display width in the particle size distribution, even if they consider it necessary, to obtain a particle size distribution with required accuracy, or cannot widen a division width used for the operation to increase operation speed.
In addition, there is no definite criteria for determining such operation and display sections and, in many cases, the width and number of operation display sections vary depending on the apparatus. Thus, unified criteria cannot be expected. Besides, the display formats for displaying operation results differ among equipment, that is, the formats for displaying the horizontal scales not only linearly but also logarithmically differ among equipment, and users cannot freely select a display format. In other words, the users cannot compare the display of a particle size distribution outputted by one equipment with that by another at all.